Soliton Solutions Of Two Generalized Short Pulse Equations

Hone et al.obtained 8 generalized short pulse equations by applying the method of infinitely many to a special classification of second-order partial differential equations.In general,one can not construct multi-soliton solutions of these generalized short pulse equation via the classical methods directly.We choose the way of combining reciprocal transformations,which connect the generalized short pulse equations with some classical integrable flows,with Darboux transformations.In this paper,we are interested in two of the generalized short pulse equations,and want to obtain multi-soliton solutions of them.The paper is organized as follows.Firstly,we will connect the two generalized short pulse equations and its Lax pairs with the negative Kd V equation and the negative SK equation and its Lax pairs via two reciprocal transformations respectively.Secondly,we will construct multi-soliton solutions of the negative Kd V and the negative SK by Darboux transformations.Finally,multi-soliton solution of the two generalized short pulse equations are obtained by applying inverse transformations of the above reciprocal transformations to multisoliton solutions of the negative Kd V and the negative SK.Furthermore,the single soliton and two-soliton solutions of these equations are depicted.